In a wireless system, such as a digital audio broadcasting (DAB) system, a digital television system, a wireless local area network, and a wireless asynchronous transfer mode (ATM) system, signals are superimposed onto a carrier wave through signal modulation. Due to the existence of multiple paths between the transmitter and receiver, a signal may arrive at the receiver at different times and therefore, the receiver may receive multiple copies of the signal with different transmission delays. As a result, interference is generated between adjacent portions of the signal, a phenomenon known as inter-symbol interference (ISI), which limits the channel capacity of a wireless system.
One way of overcoming the ISI is an orthogonal frequency division multiplexing (OFDM) technique, which utilizes a plurality of sub-carriers. In an OFDM-based system, a serial data stream is converted into a plurality of parallel data symbols, each data symbol modulating one of the sub-carriers. All the sub-carriers as modulated by the data symbols are then multiplexed onto a carrier frequency, constituting a stream of OFDM symbols, wherein each of the OFDM symbols contains a serial stream of time-domain samples and corresponds to a symbol duration equal to the period of the carrier frequency. The serial stream of samples in each OFDM symbol are then transmitted during the corresponding symbol duration. A guard interval, or a prefix, may be introduced at one or both edges of the OFDM symbols such that ISI only takes place at the guard interval. When the receiver receives the OFDM symbols, the guard interval is removed before the useful data is processed, thereby reducing the effect of ISI.
The sub-carriers in an OFDM system are so spaced from each other that an orthogonality exists between every two sub-carriers, i.e., an integral of a product of any two sub-carriers over a cycle of the fundamental frequency is equal to zero. Accordingly, an inter-carrier interference (“ICI”), which indicates a cross-talk between two sub-carriers, is in theory eliminated. However, if an arbitrary guard interval is introduced into an OFDM symbol, orthogonality between inter-carriers is lost and ICI is not eliminated. A conventional solution is to use a cyclic extension of the OFDM symbol as the guard interval to preserve the orthogonality.
Other than the above-mentioned ISI and ICI, a signal transmitted in an OFDM system may experience other distortions, in amplitude and/or in phase. The causes for such distortions include channel effect, carrier frequency offset, and sampling frequency offset, etc. Both carrier frequency offset and sampling frequency offset result in a phase distortion and ICI.
The distortions due to the channel effect, carrier frequency offset, and sampling frequency offset may be eliminated by an equalizer that modifies the amplitude and/or phase of the received data adaptively, for example, by multiplying the received data with a coefficient that includes an amplitude compensation factor and/or a phase compensation factor. An OFDM system may incorporate training sequences, which may be used to determine the compensation factors. The training sequences may be introduced in the OFDM system as a preamble, which is inserted before the transmission of actual data, or as pilot data symbols, which are periodically inserted either in certain sub-carriers of each OFDM symbol or in all of the sub-carriers for a specific period.
Three conventional equalizers are generally known: a time-domain equalizer that operates solely in the time domain, a frequency-domain equalizer that operates solely in the frequency domain, and a time-frequency hybrid equalizer that operates in both time and frequency domains. Due to the inherent characteristics of the OFDM technique, a frequency-domain equalizer is preferred.
However, conventional equalizers generally address only one cause of the distortion. Moreover, to obtain the coefficients, a conventional equalizer either directly divides the expected symbol data by the received symbol data, or estimates the coefficients through a digital signal processing (DSP) algorithm, e.g., least-mean-square (LMS) estimate. As is known in the art, division operations are difficult to implement in hardware, and the LMS estimate requires a lengthy iterative process.